Internal Inertial-Gravity Waves in a Polytropic Atmosphere

Abstract

The work is devoted to the dynamics of propagation of internal gravity waves on a planetary scale in a polytropic atmosphere. Thus, in the work the problem is solved in the traditional approximation, when the horizontal component of the Coriolis inertia force is not taken into account. As always in such a situation, there are two restoring forces: one is the buoyancy force, and the other is the Coriolis inertial force. Therefore, there is a spectrum of frequencies from inertial to the maximum frequency, which is the buoyancy frequency. The generally accepted point of view is that internal gravity waves oscillate only with the maximum frequency of buoyancy, namely the Brunt–Väisälä frequency. Let us recall that an air parcel oscillates with the Brunt–Väisälä frequency, the acceleration of which is due to a density disturbance, but the movement occurs adiabatically, i.e. with constant potential temperature. The analysis of the equations describing the dynamics of internal inertial-gravity waves carried out in this work showed that in the general case this is not the case. The frequency of oscillations depends on the adopted mathematical model that describes the dynamics of the waves. Thus, the novelty of our work lies in the fact that we consider not an adiabatic, but a polytropic process. An expression is obtained for the buoyancy frequency, which includes the specific heat capacity of the polytropic process.